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Bioimage InformaticsLecture 5, Spring 2012
Fundamentals of Fluorescence Microscopy (II)
Bioimage Data Analysis (I): Basic Operations
Lecture 5 January 25, 2012
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Outline
• Performance metrics of a microscope
• Basic image analysis: open sources of images
• Basic image analysis: image filtering
• Basic image analysis: image intensity derivative calculation
• Project assignment 1
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• Performance metrics of a microscope
• Basic image analysis: open sources of images
• Basic image analysis: image filtering
• Basic image analysis: image intensity derivative calculation
• Project assignment 1
4
Performance Metrics of a Light Microscope
• Resolution: the smallest feature distance that can be resolved.
• Field of view: the area of a specimen that can be observed and recorded in an image.
• Depth-of-field: the axial distance (depth) range in the specimen that appears in focus in an image.
• Light collection power: determines image brightness.
Basic Concept of a Linear System
• A system is said to be linear if it satisfies the following two conditions
- Homogeneity - Additivity
• A linear system can be characterized in the time domain by its impulse response.
• A properly built and aligned microscope can be accurately modeled as a linear system.
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Sr(t) y(t)
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Microscope as a Linear System
• A light microscope is a linear system whose impulse response is an Airy disk.http://micro.magnet.fsu.edu/primer/java/imageformation/airydiskformation/index.html
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Airy Disk• Airy (after George Biddell Airy) disk is the diffraction
pattern of a point feature under a circular aperture.
• It has the following form
• Detailed derivation is given in Born & Wolf, Principles of Optics, 7th ed., pp. 439-441.
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0
2J rI I
r
J1(x) is a Bessel function of the first kind.
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Microscope Image Formation: PSF & OTF• The impulse response of the microscope is called its
point spread function (PSF).
• The transfer function of a microscope is called its optical transfer function (OTF).
• The PSF of a properly built and aligned microscopy is an Airy Disk.
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Numerical Aperture• Numerical aperture (NA)
determines microscope resolution and light collection power.
NA n sin n: refractive index of the medium between
the lens and the specimen
: half of the angular aperture
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Microscope Image Formation• Microscope image formation can be modeled as
a convolution with the PSF.
I x, y O x, y psf x, y
F I x, y F O x, y F psf x, y
http://micro.magnet.fsu.edu/primer/java/mtf/airydisksize/index.html
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Different Definition of Light Microscopy Resolution Limit (Demo)
• Rayleigh limit
• Sparrow limit
http://www.microscopy.fsu.edu/primer/java/imageformation/rayleighdisks/index.html
0 61.DNA
0 47.DNA
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Field of View (Demo)• Field of view: the region that is visible under a
microscope
• If characterized in diameter
• If characterized in area
Field diaphragm diameterDM
http://micro.magnet.fsu.edu/primer/java/microscopy/diaphragm/index.html
2
2
Field diaphragm diameterSM
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Depth-of-Field• Depth-of-field: the axial distance (depth) in the specimen
that appears in focus in the image.
2totn nd e
NA M NA
n: refractive index of the medium between the lens and the specimen
: emission wavelength
M: magnification
NA: numerical aperture
e: smallest resolvable distance in the image plane
Example: Depth-of-Field
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Smaug1 mRNA-silencing foci respond to NMDA and modulate synapse formation, M. Baez, et al, JCB, 195:1141-1157, 2011
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Image Intensity: Light Collecting Power
• For transmitted light
• For epi-fluorescence
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2
NAIM
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2
NAIM
http://micro.magnet.fsu.edu/primer/anatomy/imagebrightness.html
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Working Distance
• The distance between the objective lens and the specimen.
• Working distance does not directly influence imaging but may determine how images can be collected.
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Summary: High Resolution Microscopy• Size of cellular features are typically on the scale of a
micron or smaller.
• To resolve such features require
- Shorter wavelength (e.g. electron microscopy)- High numerical aperture (for resolution)- High magnification (for spatial sampling)
0 61.DNA
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Summary: High Resolution Microscopy
• Higher magnification and higher numerical aperture mean
- Smaller field of view
- Smaller depth of field
- Lower light collection power
- Smaller working distance
2
2
Field diaphragm diameterSM
2totn nd e
NA M NA
2
2
NAIM
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• Performance metrics of a microscope
• Basic image analysis: open sources of images
• Basic image analysis: image filtering
• Basic image analysis: image intensity derivative calculation
• Project assignment 1
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A Few Words about MATLAB
• There are many excellent tutorials online.
• There are many excellent reference books.
• It is worthwhile to invest some time on learning MATLAB.
• Please bring your questions to our teaching assistant.
Anuparma KuruvillaEmail: [email protected]: C119 Hamerschlag Hall
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Where & How to Get Image Data
• The number of open image repositories is constantly increasing.
• OME: open microscopy environmenthttp://www.openmicroscopy.org/
• JCB DataViewer
• ASCB Cell Image Library
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• Performance metrics of a microscope
• Basic image analysis: open sources of images
• Basic image analysis: image filtering
• Basic image analysis: image intensity derivative calculation
• Project assignment 1
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Basic Concept of Image Filtering (I)
• Application I: noise suppression
original noise added σ=2 σ=10 σ=20
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Basic Concept of Image Filtering (II)
• Application II: image conditioning
Gonzalez & Woods, DIP 2/e
Canny, J., A Computational Approach To Edge Detection, IEEE Trans. Pattern Analysis and Machine Intelligence, 8(6):679–698, 1986.
Gonzalez & Woods, DIP 3/e
Basic Concept of Image Filtering (III)
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Basic Concept of Image Filtering (IV)
• Image filtering in the spatial domain
http://www.imageprocessingplace.com/
, , , , , ,a b a b
s a t b s a t b
w s t f x s y t w s t f x s y t w x y f x y
w(x,y)f(x,y) g(x,y)
g x, y w x, y f x, y
G u,v W u,v F u,v
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• Gaussian kernel in 1D
• First order derivative
• Second order derivative
Gaussian Filter (I)
2
221;2
x
G x e
2
223
;2
xxG x e
2
22
223
; 12
xx xG x e
2 2
2 22 21;2
x y
x y
x yx y
G x, y , e
Gaussian Filters (II)
• Some basic properties of a Gaussian filter- It is a low pass filter
- It is separable
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2 22
22
212 2
x F ee
2 2 22
2 2 222 2 221 1 1;2 2 2
x y yx
x y yx
x yx y x y
G x, y , e e e
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• Performance metrics of a microscope
• Basic image analysis: open sources of images
• Basic image analysis: image filtering
• Basic image analysis: image intensity derivative calculation
• Project assignment 1
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Combination of Noise Suppression and Gradient Estimation (I)
• Implementation
• Notation: J: raw image; I: filtered image after convolution with Gaussian kernel G.
• A basic property of convolution
1 12
1 12
x
y
I i , j I i , jI i, j
I i, j I i, jI i, j
x y
G J G JI G I GI J I Jx x x y y y
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• Performance metrics of a microscope
• Basic image analysis: open sources of images
• Basic image analysis: image filtering
• Basic image analysis: image intensity derivative calculation
• Project assignment 1
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Basic Image Operations
• Reading an imaging
• Accessing individual pixels
• Setting a region of interest (ROI)
• Writing an image
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Questions?